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sweet [91]
3 years ago
12

A 22 kg solid door is 220 cm tall, 91 cm wide. a) What is the door's moment of inertia for rotation about a vertical axis inside

the door, 15 cm from one edge? b) What is the door's moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge?
Physics
1 answer:
iris [78.8K]3 years ago
3 0

Answer

given,

mass of the solid door = 22 Kg

dimension of door = 220 cm x 91 cm

moment of inertia about the hinge

   I = \dfrac{1}{3}Mr^2

r is the distance from the one edge which is equal to 91 cm or 0.91 m

   I = \dfrac{1}{3}\times 22 \times 0.91^2

   I = 6.073\ kg m^2

Moment of inertia about center for rectangular gate is equal to

   I_{CM} = \dfrac{1}{12}Mr^2

moment of inertia for rotation about a vertical axis inside the door, 15 cm from one edge

   I = I_{CM} + MR^2

   I = I_{CM} + M(\dfrac{91}{2}- 15)^2

   I = \dfrac{1}{12}Mr^2+ M(0.0930)

  I = \dfrac{1}{12}\times 22 \times 0.91^2+ 22 \times (0.093)

  I = 3.56\ Kg m^2

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